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Harry shoots arrows at a target board. He has a $50 \%$ chance of hitting the bull's eye on each shot.

  1. $\quad$ Calculate the probability that Harry will hit the bull's eye in his first shot and his second shot.
  2. $\quad$ Calculate the probability that Harry will hit the bull's eye at least twice in his first three shots.
  3. $\quad$  Glenda also has a $50 \%$ chance of hitting the bull's eye on each shot. Harry and Glenda will take turns to shoot an arrow and the first person to hit the bull's eye will be the winner. Calculate the probability that the person who shoots first will be the winner of the challenge.
in Mathematics by Bronze Status (8,710 points) | 20 views

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Best answer

Solution 1:

Solution 2:

\begin{array}{l}
\mathrm{P} \text { (Bull's eye first shot and second shot) }\\
=0,5 \times 0,5\\
=0,25 \text { or } \frac{1}{4}
\end{array}

 

Solution 3:

\begin{array}{l}
\mathrm{P} \text { (Bull's eye at least twice in } 3 \text { shots) }\\
=(0,5 \times 0,5 \times 0,5)+(0,5 \times 0,5 \times 0,5)+(0,5 \times 0,5 \times 0,5)+\\
(0,5 \times 0,5 \times 0,5)\\
=0,125+0,125+0,125+0,125\\
=0,5 \text { or } \frac{1}{2}
\end{array}

Solution 4:

\begin{array}{l}
\text { Person shoots first: }\\
(0,5)+(0,5)^{3}+(0,5)^{5}+\ldots\\
\mathrm{P}=\frac{a}{1-r}\\
\mathrm{P}=\frac{0,5}{1-0,25}\\
\mathrm{P}=\frac{2}{3}=0,67
\end{array}

by Bronze Status (8,710 points)

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